Linear Bellman Combination for Control of Character Animation

Abstract

Controllers are necessary for physically-based
synthesis of character animation. However, creating
controllers requires either manual
tuning or expensive computer optimization.
We introduce linear Bellman combination as a method for
reusing existing controllers. Given a set of controllers for
related tasks, this combination creates a controller that performs
a new task.
It naturally weights the contribution of each component controller by
its relevance to the current state and goal of the system.
We demonstrate that linear Bellman combination outperforms naive
combination often succeeding where naive combination fails.
Furthermore, this combination is provably optimal
for a new task if the component controllers are also optimal for
related tasks. We demonstrate the applicability of linear Bellman
combination to interactive character control of stepping motions
and acrobatic maneuvers.

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Acknowledgments

This project was inspired by Emo Todorov's work on
linearly solvable Markov decision processes.
Russ Tedrake provided some early feedback on how
combination might be used in practice. Emo provided
a MATLAB implementation of his z-iteration algorithm which
allowed us to test combination on simple examples. Michiel
van de Panne provided a detailed and helpful early review of
our paper. This work was supported by grants from the
Singapore-MIT Gambit Game Lab, the National Science Foundation
(2007043041, CCF-0810888), Adobe Systems,
Pixar Animation Studios, and software
donations from Autodesk and Adobe systems.